Frequency mode excitations in two-dimensional Hindmarsh–Rose neural networks

Conrad Bertrand Tabi, Armand Sylvin Etémé, Alidou Mohamadou

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this work, we explicitly show the existence of two frequency regimes in a two-dimensional Hindmarsh–Rose neural network. Each of the regimes, through the semi-discrete approximation, is shown to be described by a two-dimensional complex Ginzburg–Landau equation. The modulational instability phenomenon for the two regimes is studied, with consideration given to the coupling intensities among neighboring neurons. Analytical solutions are also investigated, along with their propagation in the two frequency regimes. These waves, depending on the coupling strength, are identified as breathers, impulses and trains of soliton-like structures. Although the waves in two regimes appear in some common regions of parameters, some phase differences are noticed and the global dynamics of the system is highly influenced by the values of the coupling terms. For some values of such parameters, the high-frequency regime displays modulated trains of waves, while the low-frequency dynamics keeps the original asymmetric character of action potentials. We argue that in a wide range of pathological situations, strong interactions among neurons can be responsible for some pathological states, including schizophrenia and epilepsy.

Original languageEnglish
Pages (from-to)186-198
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Volume474
DOIs
Publication statusPublished - May 15 2017

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Excitation
Neural Networks
neurons
Neuron
epilepsy
schizophrenia
excitation
Modulational Instability
Epilepsy
Complex Ginzburg-Landau Equation
Breathers
Global Dynamics
Discrete Approximation
Action Potential
Phase Difference
Impulse
Low Frequency
impulses
Solitons
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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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Frequency mode excitations in two-dimensional Hindmarsh–Rose neural networks. / Tabi, Conrad Bertrand; Etémé, Armand Sylvin; Mohamadou, Alidou.

In: Physica A: Statistical Mechanics and its Applications, Vol. 474, 15.05.2017, p. 186-198.

Research output: Contribution to journalArticle

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